1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 178,928 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 178,918 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     65
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    100
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     14
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      7
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      1
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      8
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      4
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      5
## 116  2020-06-24          East of England      4
## 117  2020-06-25          East of England      1
## 118  2020-06-26          East of England      5
## 119  2020-06-27          East of England      6
## 120  2020-06-28          East of England      8
## 121  2020-06-29          East of England      4
## 122  2020-06-30          East of England      5
## 123  2020-07-01          East of England      2
## 124  2020-07-02          East of England      5
## 125  2020-07-03          East of England      0
## 126  2020-07-04          East of England      3
## 127  2020-07-05          East of England      1
## 128  2020-07-06          East of England      2
## 129  2020-07-07          East of England      2
## 130  2020-07-08          East of England      0
## 131  2020-07-09          East of England      8
## 132  2020-07-10          East of England      4
## 133  2020-07-11          East of England      2
## 134  2020-07-12          East of England      1
## 135  2020-07-13          East of England      7
## 136  2020-07-14          East of England      2
## 137  2020-07-15          East of England      0
## 138  2020-07-16          East of England      0
## 139  2020-07-17          East of England      0
## 140  2020-03-01                   London      0
## 141  2020-03-02                   London      0
## 142  2020-03-03                   London      0
## 143  2020-03-04                   London      0
## 144  2020-03-05                   London      0
## 145  2020-03-06                   London      1
## 146  2020-03-07                   London      0
## 147  2020-03-08                   London      0
## 148  2020-03-09                   London      1
## 149  2020-03-10                   London      0
## 150  2020-03-11                   London      5
## 151  2020-03-12                   London      6
## 152  2020-03-13                   London     10
## 153  2020-03-14                   London     13
## 154  2020-03-15                   London      9
## 155  2020-03-16                   London     15
## 156  2020-03-17                   London     23
## 157  2020-03-18                   London     27
## 158  2020-03-19                   London     25
## 159  2020-03-20                   London     44
## 160  2020-03-21                   London     49
## 161  2020-03-22                   London     54
## 162  2020-03-23                   London     63
## 163  2020-03-24                   London     86
## 164  2020-03-25                   London    112
## 165  2020-03-26                   London    129
## 166  2020-03-27                   London    129
## 167  2020-03-28                   London    122
## 168  2020-03-29                   London    145
## 169  2020-03-30                   London    149
## 170  2020-03-31                   London    181
## 171  2020-04-01                   London    202
## 172  2020-04-02                   London    191
## 173  2020-04-03                   London    196
## 174  2020-04-04                   London    230
## 175  2020-04-05                   London    195
## 176  2020-04-06                   London    197
## 177  2020-04-07                   London    220
## 178  2020-04-08                   London    238
## 179  2020-04-09                   London    206
## 180  2020-04-10                   London    170
## 181  2020-04-11                   London    178
## 182  2020-04-12                   London    158
## 183  2020-04-13                   London    166
## 184  2020-04-14                   London    143
## 185  2020-04-15                   London    142
## 186  2020-04-16                   London    140
## 187  2020-04-17                   London    100
## 188  2020-04-18                   London    101
## 189  2020-04-19                   London    103
## 190  2020-04-20                   London     95
## 191  2020-04-21                   London     94
## 192  2020-04-22                   London    109
## 193  2020-04-23                   London     77
## 194  2020-04-24                   London     71
## 195  2020-04-25                   London     58
## 196  2020-04-26                   London     53
## 197  2020-04-27                   London     51
## 198  2020-04-28                   London     44
## 199  2020-04-29                   London     45
## 200  2020-04-30                   London     40
## 201  2020-05-01                   London     41
## 202  2020-05-02                   London     41
## 203  2020-05-03                   London     36
## 204  2020-05-04                   London     30
## 205  2020-05-05                   London     25
## 206  2020-05-06                   London     37
## 207  2020-05-07                   London     37
## 208  2020-05-08                   London     30
## 209  2020-05-09                   London     23
## 210  2020-05-10                   London     26
## 211  2020-05-11                   London     18
## 212  2020-05-12                   London     18
## 213  2020-05-13                   London     17
## 214  2020-05-14                   London     20
## 215  2020-05-15                   London     18
## 216  2020-05-16                   London     14
## 217  2020-05-17                   London     15
## 218  2020-05-18                   London     10
## 219  2020-05-19                   London     14
## 220  2020-05-20                   London     19
## 221  2020-05-21                   London     12
## 222  2020-05-22                   London     10
## 223  2020-05-23                   London      6
## 224  2020-05-24                   London      7
## 225  2020-05-25                   London      9
## 226  2020-05-26                   London     13
## 227  2020-05-27                   London      7
## 228  2020-05-28                   London      8
## 229  2020-05-29                   London      7
## 230  2020-05-30                   London     12
## 231  2020-05-31                   London      6
## 232  2020-06-01                   London     10
## 233  2020-06-02                   London      8
## 234  2020-06-03                   London      6
## 235  2020-06-04                   London      8
## 236  2020-06-05                   London      4
## 237  2020-06-06                   London      0
## 238  2020-06-07                   London      5
## 239  2020-06-08                   London      5
## 240  2020-06-09                   London      4
## 241  2020-06-10                   London      7
## 242  2020-06-11                   London      5
## 243  2020-06-12                   London      3
## 244  2020-06-13                   London      3
## 245  2020-06-14                   London      3
## 246  2020-06-15                   London      1
## 247  2020-06-16                   London      2
## 248  2020-06-17                   London      1
## 249  2020-06-18                   London      2
## 250  2020-06-19                   London      5
## 251  2020-06-20                   London      3
## 252  2020-06-21                   London      4
## 253  2020-06-22                   London      2
## 254  2020-06-23                   London      1
## 255  2020-06-24                   London      4
## 256  2020-06-25                   London      3
## 257  2020-06-26                   London      2
## 258  2020-06-27                   London      1
## 259  2020-06-28                   London      2
## 260  2020-06-29                   London      2
## 261  2020-06-30                   London      1
## 262  2020-07-01                   London      2
## 263  2020-07-02                   London      2
## 264  2020-07-03                   London      2
## 265  2020-07-04                   London      1
## 266  2020-07-05                   London      3
## 267  2020-07-06                   London      2
## 268  2020-07-07                   London      1
## 269  2020-07-08                   London      3
## 270  2020-07-09                   London      4
## 271  2020-07-10                   London      0
## 272  2020-07-11                   London      0
## 273  2020-07-12                   London      0
## 274  2020-07-13                   London      1
## 275  2020-07-14                   London      0
## 276  2020-07-15                   London      1
## 277  2020-07-16                   London      0
## 278  2020-07-17                   London      0
## 279  2020-03-01                 Midlands      0
## 280  2020-03-02                 Midlands      0
## 281  2020-03-03                 Midlands      1
## 282  2020-03-04                 Midlands      0
## 283  2020-03-05                 Midlands      0
## 284  2020-03-06                 Midlands      0
## 285  2020-03-07                 Midlands      0
## 286  2020-03-08                 Midlands      2
## 287  2020-03-09                 Midlands      1
## 288  2020-03-10                 Midlands      0
## 289  2020-03-11                 Midlands      2
## 290  2020-03-12                 Midlands      6
## 291  2020-03-13                 Midlands      5
## 292  2020-03-14                 Midlands      4
## 293  2020-03-15                 Midlands      5
## 294  2020-03-16                 Midlands     11
## 295  2020-03-17                 Midlands      8
## 296  2020-03-18                 Midlands     13
## 297  2020-03-19                 Midlands      8
## 298  2020-03-20                 Midlands     28
## 299  2020-03-21                 Midlands     13
## 300  2020-03-22                 Midlands     31
## 301  2020-03-23                 Midlands     33
## 302  2020-03-24                 Midlands     41
## 303  2020-03-25                 Midlands     48
## 304  2020-03-26                 Midlands     64
## 305  2020-03-27                 Midlands     72
## 306  2020-03-28                 Midlands     89
## 307  2020-03-29                 Midlands     92
## 308  2020-03-30                 Midlands     90
## 309  2020-03-31                 Midlands    123
## 310  2020-04-01                 Midlands    140
## 311  2020-04-02                 Midlands    142
## 312  2020-04-03                 Midlands    124
## 313  2020-04-04                 Midlands    151
## 314  2020-04-05                 Midlands    164
## 315  2020-04-06                 Midlands    140
## 316  2020-04-07                 Midlands    123
## 317  2020-04-08                 Midlands    186
## 318  2020-04-09                 Midlands    139
## 319  2020-04-10                 Midlands    127
## 320  2020-04-11                 Midlands    142
## 321  2020-04-12                 Midlands    139
## 322  2020-04-13                 Midlands    120
## 323  2020-04-14                 Midlands    116
## 324  2020-04-15                 Midlands    147
## 325  2020-04-16                 Midlands    102
## 326  2020-04-17                 Midlands    118
## 327  2020-04-18                 Midlands    115
## 328  2020-04-19                 Midlands     92
## 329  2020-04-20                 Midlands    107
## 330  2020-04-21                 Midlands     86
## 331  2020-04-22                 Midlands     78
## 332  2020-04-23                 Midlands    103
## 333  2020-04-24                 Midlands     79
## 334  2020-04-25                 Midlands     72
## 335  2020-04-26                 Midlands     81
## 336  2020-04-27                 Midlands     74
## 337  2020-04-28                 Midlands     68
## 338  2020-04-29                 Midlands     53
## 339  2020-04-30                 Midlands     56
## 340  2020-05-01                 Midlands     64
## 341  2020-05-02                 Midlands     51
## 342  2020-05-03                 Midlands     52
## 343  2020-05-04                 Midlands     61
## 344  2020-05-05                 Midlands     59
## 345  2020-05-06                 Midlands     59
## 346  2020-05-07                 Midlands     48
## 347  2020-05-08                 Midlands     34
## 348  2020-05-09                 Midlands     37
## 349  2020-05-10                 Midlands     42
## 350  2020-05-11                 Midlands     33
## 351  2020-05-12                 Midlands     45
## 352  2020-05-13                 Midlands     40
## 353  2020-05-14                 Midlands     38
## 354  2020-05-15                 Midlands     40
## 355  2020-05-16                 Midlands     34
## 356  2020-05-17                 Midlands     31
## 357  2020-05-18                 Midlands     36
## 358  2020-05-19                 Midlands     35
## 359  2020-05-20                 Midlands     36
## 360  2020-05-21                 Midlands     32
## 361  2020-05-22                 Midlands     27
## 362  2020-05-23                 Midlands     34
## 363  2020-05-24                 Midlands     20
## 364  2020-05-25                 Midlands     26
## 365  2020-05-26                 Midlands     33
## 366  2020-05-27                 Midlands     29
## 367  2020-05-28                 Midlands     28
## 368  2020-05-29                 Midlands     20
## 369  2020-05-30                 Midlands     21
## 370  2020-05-31                 Midlands     22
## 371  2020-06-01                 Midlands     20
## 372  2020-06-02                 Midlands     22
## 373  2020-06-03                 Midlands     24
## 374  2020-06-04                 Midlands     16
## 375  2020-06-05                 Midlands     21
## 376  2020-06-06                 Midlands     20
## 377  2020-06-07                 Midlands     17
## 378  2020-06-08                 Midlands     16
## 379  2020-06-09                 Midlands     18
## 380  2020-06-10                 Midlands     15
## 381  2020-06-11                 Midlands     13
## 382  2020-06-12                 Midlands     12
## 383  2020-06-13                 Midlands      6
## 384  2020-06-14                 Midlands     18
## 385  2020-06-15                 Midlands     12
## 386  2020-06-16                 Midlands     15
## 387  2020-06-17                 Midlands     11
## 388  2020-06-18                 Midlands     15
## 389  2020-06-19                 Midlands     10
## 390  2020-06-20                 Midlands     15
## 391  2020-06-21                 Midlands     14
## 392  2020-06-22                 Midlands     14
## 393  2020-06-23                 Midlands     16
## 394  2020-06-24                 Midlands     15
## 395  2020-06-25                 Midlands     18
## 396  2020-06-26                 Midlands      5
## 397  2020-06-27                 Midlands      5
## 398  2020-06-28                 Midlands      7
## 399  2020-06-29                 Midlands      6
## 400  2020-06-30                 Midlands      6
## 401  2020-07-01                 Midlands      7
## 402  2020-07-02                 Midlands      9
## 403  2020-07-03                 Midlands      3
## 404  2020-07-04                 Midlands      4
## 405  2020-07-05                 Midlands      6
## 406  2020-07-06                 Midlands      5
## 407  2020-07-07                 Midlands      3
## 408  2020-07-08                 Midlands      5
## 409  2020-07-09                 Midlands      8
## 410  2020-07-10                 Midlands      3
## 411  2020-07-11                 Midlands      0
## 412  2020-07-12                 Midlands      5
## 413  2020-07-13                 Midlands      1
## 414  2020-07-14                 Midlands      1
## 415  2020-07-15                 Midlands      6
## 416  2020-07-16                 Midlands      1
## 417  2020-07-17                 Midlands      0
## 418  2020-03-01 North East and Yorkshire      0
## 419  2020-03-02 North East and Yorkshire      0
## 420  2020-03-03 North East and Yorkshire      0
## 421  2020-03-04 North East and Yorkshire      0
## 422  2020-03-05 North East and Yorkshire      0
## 423  2020-03-06 North East and Yorkshire      0
## 424  2020-03-07 North East and Yorkshire      0
## 425  2020-03-08 North East and Yorkshire      0
## 426  2020-03-09 North East and Yorkshire      0
## 427  2020-03-10 North East and Yorkshire      0
## 428  2020-03-11 North East and Yorkshire      0
## 429  2020-03-12 North East and Yorkshire      0
## 430  2020-03-13 North East and Yorkshire      0
## 431  2020-03-14 North East and Yorkshire      0
## 432  2020-03-15 North East and Yorkshire      2
## 433  2020-03-16 North East and Yorkshire      3
## 434  2020-03-17 North East and Yorkshire      1
## 435  2020-03-18 North East and Yorkshire      2
## 436  2020-03-19 North East and Yorkshire      6
## 437  2020-03-20 North East and Yorkshire      5
## 438  2020-03-21 North East and Yorkshire      6
## 439  2020-03-22 North East and Yorkshire      7
## 440  2020-03-23 North East and Yorkshire      9
## 441  2020-03-24 North East and Yorkshire      8
## 442  2020-03-25 North East and Yorkshire     18
## 443  2020-03-26 North East and Yorkshire     21
## 444  2020-03-27 North East and Yorkshire     28
## 445  2020-03-28 North East and Yorkshire     35
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## 959  2020-07-03               South West      0
## 960  2020-07-04               South West      0
## 961  2020-07-05               South West      1
## 962  2020-07-06               South West      0
## 963  2020-07-07               South West      0
## 964  2020-07-08               South West      2
## 965  2020-07-09               South West      0
## 966  2020-07-10               South West      1
## 967  2020-07-11               South West      0
## 968  2020-07-12               South West      0
## 969  2020-07-13               South West      1
## 970  2020-07-14               South West      0
## 971  2020-07-15               South West      0
## 972  2020-07-16               South West      0
## 973  2020-07-17               South West      1

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-07-16"

The completion date of the NHS Pathways data is Thursday 16 Jul 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -13.4497   -4.4186   -0.5333    3.7771    8.4265  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.581e+00  6.484e-02   70.66   <2e-16 ***
## note_lag    1.465e-05  6.754e-07   21.70   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 24.50891)
## 
##     Null deviance: 12504.0  on 77  degrees of freedom
## Residual deviance:  1966.4  on 76  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##   97.660691    1.000015
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 85.832506 110.677533
## note_lag     1.000013   1.000016

Rsq(lag_mod)
## [1] 0.8427369

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1474.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.3         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.4.2          webshot_0.5.2     httr_1.4.1       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.7       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-8         zip_2.0.4         magrittr_1.5      kyotil_2019.11-22
## [41] Matrix_1.2-18     Rcpp_1.0.5        munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.6      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.12.8 modelr_0.1.8      vctrs_0.3.2       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.15        
## [77] openxlsx_4.1.5    broom_0.7.0       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1